Population-shrinkage of covariance to estimate better brain functional connectivity

Abstract : Brain functional connectivity, obtained from functional Magnetic Resonance Imaging at rest (r-fMRI), reflects inter-subject variations in behavior and characterizes neuropathologies. It is captured by the covariance matrix between time series of remote brain regions. With noisy and short time series as in r-fMRI, covariance estimation calls for penalization, and shrinkage approaches are popular. Here we introduce a new covariance estimator based on a non-isotropic shrinkage that integrates prior knowledge of the covariance distribution over a large population. The estimator performs shrinkage tailored to the Riemannian geometry of symmetric positive definite matrices, coupled with a probabilistic modeling of the subject and population covariance distributions. Experiments on a large-scale dataset show that such estimators resolve better intra-and inter-subject functional connectivities compared existing co-variance estimates. We also demonstrate that the estimator improves the relationship across subjects between their functional-connectivity measures and their behavioral assessments.
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Mehdi Rahim, Bertrand Thirion, Gaël Varoquaux. Population-shrinkage of covariance to estimate better brain functional connectivity. Medical Image Computing and Computer Assisted Interventions, Sep 2017, Quebec city, Canada. ⟨hal-01547612⟩

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